A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We can write a formula for the th term of a geometric sequence in the form
where is the common ratio between successive terms.
is a geometric sequence where each term is times the previous term.
A formula for the th term of the sequence is
is a geometric series where each term is times the previous term.
A formula for the th term of this sequence is
is not a geometric sequence. The first ratio is , but the second ratio is .
No formula of the form
can be written for this sequence.
See also arithmetic sequences.